1. ## Geometric Series Equivalence

Hello,
Why is this:

Equivalent to this:

Thank you.

2. ## Re: Geometric Series Equivalence

Since summations only work with integers, you can replace the log(n) parts with an integer, such as k. The write a proof by induction to show that

$\displaystyle \sum _{i=0} ^{k-1} 2^i = 2^k-1$

3. ## Re: Geometric Series Equivalence

we expect $\displaystyle \sum _{i=0}^{\text{Log} n-1} 2^i$ to be an integer

but $\displaystyle 2^{\text{Log} n}-1$ is not necessarily an integer